ARPACK is a collection of Fortran77 subroutines designed to solve large
scale eigenvalue problems.

The package is designed to compute a few eigenvalues and corresponding
eigenvectors of a general n by n matrix A. It is most appropriate for
large sparse or structured matrices A where structured means that a
matrix-vector product w <- Av requires order n rather than the usual
order n2 floating point operations. This software is based upon an
algorithmic variant of the Arnoldi process called the Implicitly
Restarted Arnoldi Method (IRAM). When the matrix A is symmetric it
reduces to a variant of the Lanczos process called the Implicitly
Restarted Lanczos Method (IRLM). These variants may be viewed as a
synthesis of the Arnoldi/Lanczos process with the Implicitly Shifted QR
technique that is suitable for large scale problems. For many standard
problems, a matrix factorization is not required. Only the action of the
matrix on a vector is needed.

ARPACK software is capable of solving large scale symmetric,
nonsymmetric, and generalized eigenproblems from significant application
areas. The software is designed to compute a few (k) eigenvalues with
user specified features such as those of largest real part or largest
magnitude. Storage requirements are on the order of n*k locations. No
auxiliary storage is required. A set of Schur basis vectors for the
desired k-dimensional eigen-space is computed which is numerically
orthogonal to working precision. Numerically accurate eigenvectors are
available on request.
